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Event-related fMRI (er-fMRI) Methods & models for fMRI data analysis November 2012 With many thanks for slides & images to: FIL Methods group, particularly Rik Henson and Christian Ruff Klaas Enno Stephan Translational Neuromodeling Unit (TNU) Institute for Biomedical Engineering, University of Zurich & ETH Zurich Laboratory for Social & Neural Systems Research (SNS), University of Zurich Wellcome Trust Centre for Neuroimaging, University College London

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Overview of SPM RealignmentSmoothing Normalisation General linear model Statistical parametric map (SPM) Image time-series Parameter estimates Design matrix Template Kernel Gaussian field theory p <0.05 Statisticalinference

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Overview 1. Advantages of er-fMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal basis functions 5. Timing issues 6. Design optimisation 7. Nonlinearities at short SOAs

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Advantages of er-fMRI 1.Randomised trial order c.f. confounds of blocked designs

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Pleasant (P) Unpleasant (U) Blocked designs may trigger expectations and cognitive sets … Intermixed designs can minimise this by stimulus randomisation ……… … … er-fMRI: Stimulus randomisation Unpleasant (U) Pleasant (P)

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Advantages of er-fMRI 1.Randomised trial order c.f. confounds of blocked designs 2.Post hoc classification of trials e.g. according to performance or subsequent memory

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er-fMRI: post-hoc classification of trials Gonsalves & Paller (2000) Nature Neuroscience Items with wrong memory of picture („hat“) were associated with more occipital activity at encoding than items with correct rejection („brain“) „was shown as picture“ „was not shown as picture“ Participant response:

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Advantages of er-fMRI 1.Randomised trial order c.f. confounds of blocked designs 2.Post hoc classification of trials e.g. according to performance or subsequent memory 3.Some events can only be indicated by the subject e.g. spontaneous perceptual changes

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eFMRI: “on-line” event-definition Bistable percepts Binocular rivalry

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Advantages of er-fMRI 1.Randomised trial order c.f. confounds of blocked designs 2.Post hoc classification of trials e.g. according to performance or subsequent memory 3.Some events can only be indicated by the subject e.g. spontaneous perceptual changes 4.Some trials cannot be blocked e.g. “oddball” designs

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time … er-fMRI: “oddball” designs

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Advantages of er-fMRI 1.Randomised trial order c.f. confounds of blocked designs 2.Post hoc classification of trials e.g. according to performance or subsequent memory 3.Some events can only be indicated by subject e.g. spontaneous perceptual changes 4.Some trials cannot be blocked e.g. “oddball” designs 5.More accurate models even for blocked designs? “state-item” interactions

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P1P2P3 “Event” model may capture state-item interactions U1U2U3 “Epoch” model assumes constant neural processes throughout block U1U2U3 P1P2 P3 er-fMRI: “event-based” model of block-designs Data Model

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Convolved with HRF Series of events Delta functions Designs can be blocked or intermixed, Designs can be blocked or intermixed, BUT models for blocked designs can be BUT models for blocked designs can be epoch- or event-related epoch- or event-related Epochs are periods of sustained stimulation (e.g, box-car functions)Epochs are periods of sustained stimulation (e.g, box-car functions) Events are impulses (delta-functions)Events are impulses (delta-functions) Near-identical regressors can be created by 1) sustained epochs, 2) rapid series of events (SOAs<~3s)Near-identical regressors can be created by 1) sustained epochs, 2) rapid series of events (SOAs<~3s) In SPM, all conditions are specified in terms of their 1) onsets and 2) durationsIn SPM, all conditions are specified in terms of their 1) onsets and 2) durations … epochs: variable or constant duration … epochs: variable or constant duration … events: zero duration … events: zero duration “Classic” Boxcar function Sustained epoch Modeling block designs: epochs vs events

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Disadvantages of er-fMRI 1.Less efficient for detecting effects than blocked designs. 2.Some psychological processes may be better blocked (e.g. task-switching, attentional instructions).

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Function of blood volume and deoxyhemoglobin content (Buxton et al. 1998) Peak (max. oxygenation) 4-6s post-stimulus; return to baseline after 20-30s initial undershoot sometimes observed (Malonek & Grinvald, 1996) Similar across V1, A1, S1… … but differences across other regions (Schacter et al. 1997) and individuals (Aguirre et al. 1998) BOLD impulse response Brief Stimulus Undershoot Initial Undershoot Peak

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Early er-fMRI studies used a long Stimulus Onset Asynchrony (SOA) to allow BOLD response to return to baseline. However, if the BOLD response is explicitly modelled, overlap between successive responses at short SOAs can be accommodated… … particularly if responses are assumed to superpose linearly. Short SOAs can give a more efficient design (see below). BOLD impulse response Brief Stimulus Undershoot Initial Undershoot Peak

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General Linear (Convolution) Model For block designs, the exact shape of the convolution kernel (i.e. HRF) does not matter much. For event-related designs this becomes much more important. Usually, we use more than a single basis function to model the HRF. GLM for a single voxel: y(t) = u(t) h( ) + (t) Design Matrix convolution T 2T 3T... u(t) h( )= ß i f i ( ) sampled each scan

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Temporal basis functions Finite Impulse Response (FIR) model Fourier basis set Gamma functions set Informed basis set

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Canonical HRF (2 gamma functions) plus Multivariate Taylor expansion in: time (Temporal Derivative) width (Dispersion Derivative) F-tests allow testing for any responses of any shape. T-tests on canonical HRF alone (at 1 st level) can be improved by derivatives reducing residual error, and can be interpreted as “amplitude” differences, assuming canonical HRF is a reasonable fit. Canonical Temporal Dispersion Friston et al. 1998, NeuroImage

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Temporal basis sets: Which one? + FIR+ Dispersion+ TemporalCanonical canonical + temporal + dispersion derivatives appear sufficient may not be for more complex trials (e.g. stimulus-delay-response) but then such trials better modelled with separate neural components (i.e. activity no longer delta function) (Zarahn, 1999) In this example (rapid motor response to faces, Henson et al, 2001)…

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Penny et al. 2007, Hum. Brain Mapp. right occipital cortex left occipital cortex

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Timing Issues : Practical Assume TR is 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signal Scans TR=4s Stimulus (synchronous) Sampling rate=4s SOA = Stimulus onset asynchrony (= time between onsets of two subsequent stimuli)

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Timing Issues : Practical Assume TR is 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signal Higher effective sampling by: –1. Asynchrony, e.g. SOA = 1.5 TR Scans TR=4s Stimulus (asynchronous) Sampling rate=2s SOA = Stimulus onset asynchrony (= time between onsets of two subsequent stimuli)

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Timing Issues : Practical Assume TR is 4s Sampling at [0,4,8,12…] post- stimulus may miss peak signal Higher effective sampling by: –1. Asynchrony, e.g. SOA = 1.5 TR –2. Random jitter, e.g. SOA = (2 ± 0.5) TR Better response characterisation (Miezin et al, 2000) Scans TR=4s Stimulus (random jitter) Sampling rate=2s SOA = Stimulus onset asynchrony (= time between onsets of two subsequent stimuli)

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Slice-timing T=16, TR=2s Scan 0 1 o T 0 =9 o T 0 =16

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Slice-timing Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices Solutions: 1. Temporal interpolation of data … but less good for longer TRs 2. More general basis set (e.g. with temporal derivatives) … but more complicated design matrix Derivative SPM{F} Interpolated SPM{t} Bottom slice Top slice SPM{t} TR=3s Henson et al. 1999

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Design efficiency The aim is to minimize the standard error of a t-contrast (i.e. the denominator of a t-statistic). This is equivalent to maximizing the efficiency ε : Noise variance Design variance If we assume that the noise variance is independent of the specific design: This is a relative measure: all we can say is that one design is more efficient than another (for a given contrast). NB: efficiency depends on design matrix and the chosen contrast !

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= Fixed SOA = 16s Not particularly efficient… Stimulus (“Neural”)HRFPredicted Data

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= Fixed SOA = 4s Very inefficient… Stimulus (“Neural”)HRFPredicted Data

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= Randomised, SOA min = 4s More efficient … Stimulus (“Neural”)HRFPredicted Data

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= Blocked, SOA min = 4s Even more efficient… Stimulus (“Neural”)HRFPredicted Data

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Another perspective on efficiency efficiency = bandpassed signal energy Hemodynamic transfer function (based on canonical HRF): neural activity (Hz) → BOLD Highpass-filtered Josephs & Henson 1999, Phil Trans B

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= Blocked, epoch = 20s = Blocked-epoch (with short SOA) Stimulus (“Neural”)HRFPredicted Data

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= Sinusoidal modulation, f = 1/33s = The most efficient design of all! Stimulus (“Neural”)HRFPredicted Data

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= Blocked (80s), SOA min =4s, highpass filter = 1/120s Don’t use long (>60s) blocks! = Stimulus (“Neural”)HRF Predicted data (incl. HP filtering!)

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Randomised, SOA min =4s, highpass filter = 1/120s = = Randomised design spreads power over frequencies. Stimulus (“Neural”)HRFPredicted Data

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4s smoothing; 1/60s highpass filtering Efficiency: Multiple event types Design parametrised by: SOA min Minimum SOA p i (h) Probability of event-type i given history h of last m events With n event-types p i (h) is a n m n Transition Matrix Example: Randomised AB AB A0.50.5 B0.50.5 => ABBBABAABABAAA... Differential Effect (A-B) Common Effect (A+B)

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4s smoothing; 1/60s highpass filtering Example: Null events AB A0.330.33 B0.330.33 => AB-BAA--B---ABB... Efficient for differential and main effects at short SOA Equivalent to stochastic SOA (null event corresponds to a third unmodelled event-type) Null Events (A+B) Null Events (A-B) Efficiency: Multiple event types

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Efficiency – main conclusions Optimal design for one contrast may not be optimal for another. Generally, blocked designs with short SOAs are the most efficient design. With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for common effect (A+B) is 16-20s. Inclusion of null events gives good efficiency for both common and differential effects at short SOAs.

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But beware: Nonlinearities at short SOAs Friston et al. 2000, NeuroImage Friston et al. 1998, Magn. Res. Med. stim. presented alone stim. when preceded by another stim. (1 s)

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Thank you

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